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 A135037 Sums of the products of n consecutive triples of numbers. 1
 0, 60, 396, 1386, 3570, 7650, 14490, 25116, 40716, 62640, 92400, 131670, 182286, 246246, 325710, 423000, 540600, 681156, 847476, 1042530, 1269450, 1531530, 1832226, 2175156, 2564100, 3003000, 3495960, 4047246, 4661286, 5342670 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS G. C. Greubel, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1). FORMULA a(1) = 0*1*2, a(2) = 0*1*2 + 3*4*5, ..., a(n) = 0*1*2 + 3*4*5 + 6*7*8 + ... + (2n-1)*(2n)*(2n+1). a(n) = (27*n^4 - 18*n^3 - 15*n^2 + 6*n)/4. From R. J. Mathar, Feb 14 2008: (Start) O.g.f.: 6*x^2*(10+16*x+x^2)/(1-x)^5. a(n) = 6*A024391(n-1). (End) E.g.f.: (3/4)*x^2*(40 + 48*x + 9*x^2)*exp(x). - G. C. Greubel, Sep 17 2016 EXAMPLE For n = 3, the sum of the first 3 triples is 0*1*2+3*4*5+6*7*8 =396, the 3rd entry in the sequence. MATHEMATICA Table[(27 n^4 - 18 n^3 - 15 n^2 + 6 n)/4, {n, 1, 50}] (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {0, 60, 396, 1386, 3570}, 25] (* G. C. Greubel, Sep 17 2016 *) PROG (PARI) sumprod3(n) = { local(x, s=0); forstep(x=0, n, 3, s+=x*(x+1)*(x+2); print1(s", ") ) } (MAGMA) [(27*n^4-18*n^3-15*n^2+6*n)/4: n in [1..40]]; // Vincenzo Librandi, Sep 18 2016 CROSSREFS Sequence in context: A056419 A060489 A088942 * A020868 A223461 A088943 Adjacent sequences:  A135034 A135035 A135036 * A135038 A135039 A135040 KEYWORD nonn,easy AUTHOR Cino Hilliard, Feb 10 2008 STATUS approved

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Last modified June 23 02:28 EDT 2021. Contains 345395 sequences. (Running on oeis4.)