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A178440 Convolution square of A058187, the tetrahedral series with repeats. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 13 04:01 EDT 2020. Contains 335673 sequences. (Running on oeis4.)