A081586 Fourth row of Pascal-(1,3,1) array A081578.

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

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