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 A113435 a(n) = a(n-1) + Sum_{k=0..n/3} a(n-3k) with a(0)=1. 7
 1, 1, 1, 2, 3, 4, 7, 11, 16, 26, 41, 62, 98, 154, 237, 371, 581, 901, 1406, 2197, 3418, 5329, 8317, 12956, 20196, 31501, 49096, 76532, 119338, 186029, 289997, 452141, 704861, 1098826, 1713111, 2670692, 4163483, 6490879, 10119152, 15775426 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS If presented in three rows a(3n), a(3n+1) and a(3n+2) each term is the sum of the previous term in the sequence and the partial sum of its row. LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Jia Huang, Partially Palindromic Compositions, J. Int. Seq. (2023) Vol. 26, Art. 23.4.1. See pp. 4, 19. Index entries for linear recurrences with constant coefficients, signature (1,0,2,-1). FORMULA a(n) = a(n-1) + 2*a(n-3) - a(n-4) = 7*a(n-3) - 5*a(n-6) + 11*a(n-9) - a(n-12). G.f.: (1-x^3)/(1-x-2*x^3+x^4). G.f.: 1/(1-x) + x^3*Q(0)/(2-2*x) , where Q(k) = 1 + 1/(1 - x*(4*k+1 + 2*x^2 - x^3)/( x*(4*k+3 + 2*x^2 - x^3 ) + 1/Q(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Sep 11 2013 MATHEMATICA CoefficientList[Series[(1 - x^3)/(1 - x - 2*x^3 + x^4), {x, 0, 50}], x] (* G. C. Greubel, Mar 10 2017 *) LinearRecurrence[{1, 0, 2, -1}, {1, 1, 1, 2}, 40] (* Harvey P. Dale, Dec 17 2023 *) PROG (PARI) x='x+O(x^50); Vec((1 - x^3)/(1 - x - 2*x^3 + x^4)) \\ G. C. Greubel, Mar 10 2017 CROSSREFS Cf. A113439, A113444, A028495. Partial sums of A176848. Sequence in context: A120415 A023361 A210518 * A367667 A222022 A025048 Adjacent sequences: A113432 A113433 A113434 * A113436 A113437 A113438 KEYWORD nonn AUTHOR Floor van Lamoen, Nov 04 2005 STATUS approved

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Last modified May 18 08:32 EDT 2024. Contains 372618 sequences. (Running on oeis4.)