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 A101357 Partial sums of A060354. 4
 0, 1, 3, 9, 25, 60, 126, 238, 414, 675, 1045, 1551, 2223, 3094, 4200, 5580, 7276, 9333, 11799, 14725, 18165, 22176, 26818, 32154, 38250, 45175, 53001, 61803, 71659, 82650, 94860, 108376, 123288, 139689, 157675, 177345, 198801, 222148, 247494 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The Ca4 triangle sums of A139600 are given by the terms of this sequence. For the definitions of the Ca4 and other triangle sums see A180662. - Johannes W. Meijer, Apr 29 2011 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..10000 Eric Weisstein's World of Mathematics, Polygonal number Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1). FORMULA a(n) = Sum_{i=0..n} (i(i-2)^2 + i^2)/2. a(n) = A004255(n), n > 0. - R. J. Mathar, Sep 02 2008 a(n) = binomial(n+3,4) - 2*binomial(n+2,4) + 4*binomial(n+1,4). a(n) = (n^4 - 2*n^3 + 3*n^2 + 6*n)/8. - Johannes W. Meijer, Apr 29 2011 G.f.: -x*(4*x^2 - 2*x + 1) / (x-1)^5. - Colin Barker, Apr 29 2013 MATHEMATICA Table[Sum[(i*(i - 2)^2 + i^2)/2, {i, 0, n}], {n, 0, 38}] Accumulate[Table[(n (n-2)^2+n^2)/2, {n, 0, 50}]] (* Harvey P. Dale, Aug 05 2011 *) PROG (Magma) [(n^4-2*n^3+3*n^2+6*n)/8: n in [0..40]]; // Vincenzo Librandi, Aug 06 2011 (PARI) a(n)=(n^4-2*n^3+3*n^2+6*n)/8 \\ Charles R Greathouse IV, Oct 16 2015 CROSSREFS Cf. A060354, A000332. Sequence in context: A005209 A112522 A005262 * A004255 A065971 A145127 Adjacent sequences: A101354 A101355 A101356 * A101358 A101359 A101360 KEYWORD easy,nonn AUTHOR Jonathan Vos Post, Dec 25 2004 EXTENSIONS More terms from Joshua Zucker, May 12 2006 Edited by Stefan Steinerberger, Aug 01 2007 STATUS approved

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Last modified December 11 02:45 EST 2023. Contains 367717 sequences. (Running on oeis4.)