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 A081586 Fourth row of Pascal-(1,3,1) array A081578. 3
 1, 13, 73, 245, 593, 1181, 2073, 3333, 5025, 7213, 9961, 13333, 17393, 22205, 27833, 34341, 41793, 50253, 59785, 70453, 82321, 95453, 109913, 125765, 143073, 161901, 182313, 204373, 228145, 253693, 281081, 310373, 341633, 374925, 410313, 447861 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..10000 Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1). FORMULA From Harvey P. Dale, Nov 06 2011: (Start) a(n) = (3 + 28*n - 24*n^2 + 32*n^3)/3. G.f.: (1+3*x)^3/(1-x)^4. a(0)=1, a(1)=13, a(2)=73, a(3)=245, a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). (End) E.g.f.: (1/3)*(3 + 36*x + 72*x^2 + 32*x^3)*exp(x). - G. C. Greubel, May 26 2021 MATHEMATICA Table[(3+28n-24n^2+32n^3)/3, {n, 0, 40}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {1, 13, 73, 245}, 40] (* Harvey P. Dale, Nov 06 2011 *) PROG (MAGMA) [(3+28*n-24*n^2+32*n^3)/3: n in [0..40]]; // Vincenzo Librandi, Nov 16 2011 (Sage) [(3+28*n-24*n^2+32*n^3)/3 for n in (0..40)] # G. C. Greubel, May 26 2021 CROSSREFS Cf. A081578, A081585. Sequence in context: A175361 A125258 A060886 * A143008 A107963 A006230 Adjacent sequences:  A081583 A081584 A081585 * A081587 A081588 A081589 KEYWORD easy,nonn AUTHOR Paul Barry, Mar 23 2003 STATUS approved

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Last modified June 14 08:31 EDT 2021. Contains 345018 sequences. (Running on oeis4.)