A178440 Convolution square of A058187, the tetrahedral series with repeats.

1, 2, 9, 16, 44, 72, 156, 240, 450, 660, 1122, 1584, 2508, 3432, 5148, 6864, 9867, 12870, 17875, 22880, 30888, 38896, 51272, 63648, 82212, 100776, 127908, 155040, 193800, 232560, 286824, 341088, 415701, 490314, 591261, 692208, 826804, 961400, 1138500, 1315600

Offset

0,2

Links

Table of n, a(n) for n=0..39.

Index entries for linear recurrences with constant coefficients, signature (2, 5, -12, -9, 30, 5, -40, 5, 30, -9, -12, 5, 2, -1).

Formula

Square (1 + x + 4x^2 + 4x^3 + 10x^4 + ...) = (1 + 2x + 9x^2 + ...).

G.f.: 1 / ( (1+x)^6*(x-1)^8 ). - R. J. Mathar, Jul 21 2015

Example

Antidiagonal sums of terms in the array:
.
1,.. 1,. 4,. 4,. 10,  10,...
1,.. 1,. 4,. 4,. 10,........
4,.. 4,.16,.16,.............
4,.. 4,.16,.................
10,.10,.....................
10,.........................
.
Example: a(4) = 44 = (10 + 4 + 16 + 4 + 10).

Mathematica

LinearRecurrence[{2, 5, -12, -9, 30, 5, -40, 5, 30, -9, -12, 5, 2, -1}, {1, 2, 9, 16, 44, 72, 156, 240, 450, 660, 1122, 1584, 2508, 3432}, 40] (* Harvey P. Dale, Apr 17 2020 *)

Crossrefs

Cf. A058187.

Sequence in context: A213389 A304907 A237282 * A097965 A304974 A075645

Adjacent sequences: A178437 A178438 A178439 * A178441 A178442 A178443

Keyword

nonn,easy

Author

Gary W. Adamson, Dec 22 2010

Extensions

Corrected by R. J. Mathar, Jul 21 2015

Status

approved