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 A027963 T(n,n+3), T given by A027960. 5
 1, 6, 19, 47, 101, 199, 370, 661, 1148, 1954, 3278, 5442, 8967, 14696, 23993, 39065, 63483, 103025, 167040, 270655, 438346, 709716, 1148844, 1859412, 3009181, 4869594, 7879855, 12750611, 20631713, 33383659, 54016798, 87401977, 141420392, 228824086, 370246298, 599072310, 969320643 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,2 LINKS G. C. Greubel, Table of n, a(n) for n = 3..1000 Index entries for linear recurrences with constant coefficients, signature (4,-5,1,2,-1). FORMULA G.f.: x^3*(1+2*x)/((1-x)^3*(1-x-x^2)). Differences of A027964. - Ralf Stephan, Feb 07 2004 a(n) = Lucas(n+4) - (3*n^2 + 5*n + 14)/2. MATHEMATICA t[_, 0] = 1; t[_, 1] = 3; t[n_, k_] /; (k == 2*n) = 1; t[n_, k_] := t[n, k] = t[n-1, k-2] + t[n-1, k-1]; Table[t[n, n+3], {n, 3, 33}]  (* Jean-François Alcover, Dec 27 2013 *) Table[LucasL[n+4] -(3*n^2+5*n+14)/2, {n, 3, 40}] (* G. C. Greubel, Jun 01 2019 *) PROG (PARI) {a(n) = fibonacci(n+5) + fibonacci(n+3) - (3*n^2+5*n+14)/2}; \\ G. C. Greubel, Jun 01 2019 (MAGMA) [Lucas(n+4) -(3*n^2+5*n+14)/2: n in [3..40]]; // G. C. Greubel, Jun 01 2019 (Sage) [lucas_number2(n+4, 1, -1) - (3*n^2+5*n+14)/2 for n in (3..40)] # G. C. Greubel, Jun 01 2019 (GAP) List([3..40], n-> Lucas(1, -1, n+4)[2] - (3*n^2+5*n+14)/2 ) # G. C. Greubel, Jun 01 2019 CROSSREFS Cf. A000032. Sequence in context: A070893 A272047 A267829 * A034199 A272752 A272803 Adjacent sequences:  A027960 A027961 A027962 * A027964 A027965 A027966 KEYWORD nonn AUTHOR EXTENSIONS Terms a(34) onward added by G. C. Greubel, Jun 01 2019 STATUS approved

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Last modified October 15 12:31 EDT 2019. Contains 328026 sequences. (Running on oeis4.)