A239331 - OEIS

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A239331

Square array, read by antidiagonals: column k has g.f. (1+(k-1)*x)^2/(1-x)^3.

2

1, 1, 1, 1, 3, 1, 1, 5, 6, 1, 1, 7, 13, 10, 1, 1, 9, 22, 25, 15, 1, 1, 11, 33, 46, 41, 21, 1, 1, 13, 46, 73, 79, 61, 28, 1, 1, 15, 61, 106, 129, 121, 85, 36, 1, 1, 17, 78, 145, 191, 201, 172, 113, 45, 1, 1, 19, 97, 190, 265, 301, 289, 232, 145, 55, 1, 1, 21

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,5

LINKS

Table of n, a(n) for n=0..67.

FORMULA

T(n,k) = 3*T(n-1,k) - 3*T(n-2,k) + T(n-3,k).

T(n,k) = 3*T(n,k-1) - 3*T(n,k-2) + T(n,k-3).

T(n,k) = (T(n,k-1) + T(n,k+1))/2 - A161680(n).

T(n,k) = (T(n-1,k) + T(n+1,k) - A000290(n))/2.

EXAMPLE

Square array begins:

n\k : 0......1......2......3......4......5......6......7......8......9

======================================================================

.0|| 1......1......1......1......1......1......1......1......1......1

.1|| 1......3......5......7......9.....11.....13.....15.....17.....19

.2|| 1......6.....13.....22.....33.....46.....61.....78.....97....118

.3|| 1.....10.....25.....46.....73....106....145....190....241....298

.4|| 1.....15.....41.....79....129....191....265....351....449....559

.5|| 1.....21.....61....121....201....301....421....561....721....901

.6|| 1.....28.....85....172....289....436....613....820...1057...1324

.7|| 1.....36....113....232....393....596....841...1128...1457...1828

.8|| 1.....45....145....301....513....781...1105...1485...1921...2413

.9|| 1.....55....181....379....649....991...1405...1891...2449...3079

10|| 1.....66....221....466....801...1226...1741...2346...3041...3826

11|| 1.....78....265....562....969...1486...2113...2850...3697...4654

CROSSREFS

Cf. Columns: A000012, A000217, A001844, A038764, A081585, A081587, A081589, A081591, A081593.

Cf. Rows: A000012, A005408, A028872, A100536, A239325, A069133.

Sequence in context: A073145 A245368 A354971 * A145033 A202672 A054142

Adjacent sequences: A239328 A239329 A239330 * A239332 A239333 A239334

KEYWORD

nonn,tabl

AUTHOR

Philippe Deléham, Mar 16 2014

STATUS

approved