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 A281381 a(n) = n*(n + 1)*(4*n + 5)/2. 2
 0, 9, 39, 102, 210, 375, 609, 924, 1332, 1845, 2475, 3234, 4134, 5187, 6405, 7800, 9384, 11169, 13167, 15390, 17850, 20559, 23529, 26772, 30300, 34125, 38259, 42714, 47502, 52635, 58125, 63984, 70224, 76857, 83895, 91350, 99234, 107559, 116337, 125580, 135300, 145509, 156219, 167442, 179190, 191475 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Shares its digital root, zero together with period 9: repeat [3, 3, 3, 6, 6, 6, 9, 9, 9] with A027480. Final digits cycle a length period 20: repeat [0, 9, 9, 2, 0, 5, 9, 4, 2, 5, 5, 4, 4, 7, 5, 0, 4, 9, 7, 0]. LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1). FORMULA a(n) = 2*n^3 + 9*n^2/2 + 5*n/2. a(n) = 3*A016061(n). a(n) = A006002(n+1)*(n) - A006002(n)*(n-1). a(n) = A007742(n)*(n - 1)/2. From Colin Barker, Jan 21 2017: (Start) G.f.: 3*x*(3 + x) / (1 - x)^4. a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>3. (End) MATHEMATICA Table[n (n + 1) (4 n + 5)/2, {n, 0, 45}] (* or *) CoefficientList[Series[3 x (3 + x)/(1 - x)^4, {x, 0, 45}], x] (* Michael De Vlieger, Jan 21 2017 *) PROG (PARI) concat(0, Vec(3*x*(3 + x) / (1 - x)^4 + O(x^50))) \\ Colin Barker, Jan 21 2017 (PARI) a(n) = n*(n + 1)*(4*n + 5)/2 \\ Charles R Greathouse IV, Feb 01 2017 CROSSREFS Partial sums of A195319. Cf. A006002, A007742, A016061, A027480, A281258. Sequence in context: A053181 A192608 A158447 * A226449 A299280 A023163 Adjacent sequences:  A281378 A281379 A281380 * A281382 A281383 A281384 KEYWORD nonn,easy AUTHOR Peter M. Chema, Jan 21 2017 STATUS approved

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Last modified June 24 04:50 EDT 2021. Contains 345416 sequences. (Running on oeis4.)