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 A282502 Expansion of 1/(1 - Sum_{k>=0} x^(3*k*(k+1)/2+1)). 3
 1, 1, 1, 1, 2, 3, 4, 5, 7, 10, 15, 21, 29, 40, 57, 81, 114, 159, 223, 315, 445, 626, 879, 1236, 1741, 2452, 3450, 4852, 6826, 9608, 13524, 19032, 26778, 37680, 53027, 74627, 105017, 147776, 207949, 292636, 411813, 579515, 815499, 1147585, 1614917, 2272566, 3198016, 4500318, 6332952, 8911902, 12541080 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Number of compositions (ordered partitions) into сentered triangular numbers (A005448). Conjecture: every number > 1 is the sum of at most 5 сentered triangular numbers. LINKS Eric Weisstein's World of Mathematics, Centered Triangular Number FORMULA G.f.: 1/(1 - Sum_{k>=0} x^(3*k*(k+1)/2+1)). a(n) ~ c / r^n, where r = 0.71061790420456638132596657780064392952867377958... is the root of the equation r^(5/8)*EllipticTheta(2, 0, r^(3/2)) = 2 and c = 0.478786567198436133936216342628844283927491282611910379922933700360643... . - Vaclav Kotesovec, Feb 17 2017 EXAMPLE a(7) = 5 because we have [4, 1, 1, 1], [1, 4, 1, 1], [1, 1, 4, 1], [1, 1, 1, 4] and [1, 1, 1, 1, 1, 1, 1]. MATHEMATICA nmax = 50; CoefficientList[Series[1/(1 - Sum[x^(3 k (k + 1)/2 + 1), {k, 0, nmax}]), {x, 0, nmax}], x] CROSSREFS Cf. A005448, A023361, A280950. Sequence in context: A206737 A275174 A282582 * A212463 A130080 A057496 Adjacent sequences:  A282499 A282500 A282501 * A282503 A282504 A282505 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Feb 16 2017 STATUS approved

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Last modified January 20 14:40 EST 2019. Contains 319333 sequences. (Running on oeis4.)