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 A024312 a(n) = s(1)*s(n) + s(2)*s(n-1) + ... + s(k)*s(n+1-k), where k = floor((n+1)/2)), s = (natural numbers >= 3). 17
 9, 12, 31, 38, 70, 82, 130, 148, 215, 240, 329, 362, 476, 518, 660, 712, 885, 948, 1155, 1230, 1474, 1562, 1846, 1948, 2275, 2392, 2765, 2898, 3320, 3470, 3944, 4112, 4641, 4828, 5415, 5622, 6270, 6498, 7210, 7460, 8239, 8512, 9361, 9658, 10580, 10902, 11900, 12248, 13325 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS G. C. Greubel, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (1,3,-3,-3,3,1,-1). FORMULA From G. C. Greubel, Jan 17 2022: (Start) a(n) = ( (75 + 182*n + 63*n^2 + 4*n^3) - 3*(25 + 10*n + n^2)*(-1)^n )/48. G.f.: x*(9 + 3*x - 8*x^2 - 2*x^3 + 2*x^4)/((1-x)^4 * (1+x)^3). a(n) = (-60 - 18*n + (14 + 3*n)*f(n) + 3*(4+n)*f(n)^2 - 2*f(n)^3)/6, where f(n) = floor((n+5)/2). (End) MATHEMATICA Table[Sum[j*(n-j+5), {j, 3, Floor[(n+5)/2]}], {n, 50}] (* G. C. Greubel, Jan 17 2022 *) PROG (Sage) [( (75 +182*n +63*n^2 +4*n^3) - 3*(25 +10*n +n^2)*(-1)^n )/48 for n in (1..50)] # G. C. Greubel, Jan 17 2022 (Magma) [(&+[j*(n+5-j): j in [3..Floor((n+5)/2)]]) : n in [1..50]]; // G. C. Greubel, Jan 17 2022 (PARI) a(n)=((75+182*n+63*n^2+4*n^3)-3*(25+10*n+n^2)*(-1)^n)/48 \\ Charles R Greathouse IV, Oct 21 2022 CROSSREFS Cf. A024313, A024314, A024315, A024316, A024317, A024318, A024319, A024320, A024321, A024322, A024323, A024324, A024325, A024326, A024327. Sequence in context: A340040 A195162 A216297 * A024877 A120991 A253088 Adjacent sequences: A024309 A024310 A024311 * A024313 A024314 A024315 KEYWORD nonn,easy AUTHOR Clark Kimberling STATUS approved

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Last modified October 3 09:32 EDT 2023. Contains 365854 sequences. (Running on oeis4.)