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 A213827 a(n) = n^2*(n+1)*(3*n+1)/4. 3
 0, 2, 21, 90, 260, 600, 1197, 2156, 3600, 5670, 8525, 12342, 17316, 23660, 31605, 41400, 53312, 67626, 84645, 104690, 128100, 155232, 186461, 222180, 262800, 308750, 360477, 418446, 483140, 555060, 634725 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Antidiagonal sums of the convolution array A213825. LINKS Clark Kimberling, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1). FORMULA a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). G.f.: x*(2 + 11*x + 5*x^2) / (1-x)^5. a(n) = sum( i*(n^2+i^2), i=1..n ). [Bruno Berselli, Aug 25 2014] EXAMPLE a(7) = 1*(7^2+1) + 2*(7^2+2^2) + 3*(7^2+3^2) + 4*(7^2+4^2) + 5*(7^2+5^2) + 6*(7^2+6^2) + 7*(7^2+7^2) = 2156. [Bruno Berselli, Aug 25 2014] MATHEMATICA (See A213825.) PROG (MAGMA) [(n+1)*(3*n+1)*n^2/4: n in [1..40]]; // Bruno Berselli, Aug 25 2014 (Sage) [(n+1)*(3*n+1)*n^2/4 for n in (1..40)] # Bruno Berselli, Aug 25 2014 CROSSREFS Cf. A213825. Sequence in context: A212257 A034520 A111128 * A129556 A077209 A068045 Adjacent sequences:  A213824 A213825 A213826 * A213828 A213829 A213830 KEYWORD nonn,easy AUTHOR Clark Kimberling, Jul 04 2012 EXTENSIONS Edited by N. J. A. Sloane, May 14 2020 (changed offset, changed to simpler definition from Bruno Berselli). STATUS approved

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Last modified May 15 02:21 EDT 2021. Contains 343909 sequences. (Running on oeis4.)