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 A213779 Principal diagonal of the convolution array A213778. 3
 1, 6, 15, 33, 58, 97, 146, 214, 295, 400, 521, 671, 840, 1043, 1268, 1532, 1821, 2154, 2515, 2925, 3366, 3861, 4390, 4978, 5603, 6292, 7021, 7819, 8660, 9575, 10536, 11576, 12665, 13838, 15063, 16377, 17746, 19209, 20730, 22350, 24031, 25816, 27665, 29623 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Clark Kimberling, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (2,1,-4,1,2,-1). FORMULA a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + a(n-4) + 2*a(n-5) - a(n-6). G.f.: x*(1+4*x+2*x^2+x^3) / ((1-x)^4*(1+x)^2). From Colin Barker, Jan 31 2016: (Start) a(n) = (16*n^3+30*n^2+2*(3*(-1)^n+7)*n+3*((-1)^n-1))/48. a(n) = (8*n^3+15*n^2+10*n)/24 for n even. a(n) = (8*n^3+15*n^2+4*n-3)/24 for n odd. (End) MATHEMATICA (See A213778.) LinearRecurrence[{2, 1, -4, 1, 2, -1}, {1, 6, 15, 33, 58, 97}, 80] (* Harvey P. Dale, Dec 12 2016 *) PROG (PARI) Vec(x*(1+4*x+2*x^2+x^3)/((1-x)^4*(1+x)^2) + O(x^100)) \\ Colin Barker, Jan 31 2016 CROSSREFS Cf. A213778, A213500. Sequence in context: A118734 A200895 A225278 * A051410 A083052 A333959 Adjacent sequences: A213776 A213777 A213778 * A213780 A213781 A213782 KEYWORD nonn,easy AUTHOR Clark Kimberling, Jun 21 2012 STATUS approved

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Last modified September 30 09:19 EDT 2023. Contains 365781 sequences. (Running on oeis4.)