A279283 Self-composition of the tetrahedral (or triangular pyramidal) numbers; g.f.: A(x) = G(G(x)), where G(x) = g.f. of A000292.

0, 1, 8, 52, 304, 1650, 8492, 42000, 201356, 941367, 4310480, 19395042, 85972228, 376185250, 1627518840, 6971209090, 29595604656, 124648174343, 521225809112, 2165408553994, 8942942384500, 36733935375275, 150138939637144, 610840125062072, 2474686297520984, 9986301300789540

Offset

0,3

Links

Table of n, a(n) for n=0..25.

N. J. A. Sloane, Transforms

Eric Weisstein's World of Mathematics, Tetrahedral Number

Index to sequences related to pyramidal numbers

Index entries for linear recurrences with constant coefficients, signature (20,-174,876,-2885,6708,-11612,15476,-16206,13468,-8894,4632,-1868,564,-120,16,-1).

Formula

G.f.: x*(1 - x)^12/(1 - 5*x + 6*x^2 - 4*x^3 + x^4)^4.

Mathematica

CoefficientList[Series[x (1 - x)^12/(1 - 5 x + 6 x^2 - 4 x^3 + x^4)^4, {x, 0, 25}], x]
LinearRecurrence[{20, -174, 876, -2885, 6708, -11612, 15476, -16206, 13468, -8894, 4632, -1868, 564, -120, 16, -1}, {0, 1, 8, 52, 304, 1650, 8492, 42000, 201356, 941367, 4310480, 19395042, 85972228, 376185250, 1627518840, 6971209090}, 40] (* Harvey P. Dale, Jul 26 2018 *)

Crossrefs

Cf. A000292, A030280.

Sequence in context: A000432 A153336 A080279 * A257285 A125345 A111996

Adjacent sequences: A279280 A279281 A279282 * A279284 A279285 A279286

Keyword

nonn,easy

Author

Ilya Gutkovskiy, Dec 09 2016

Status

approved