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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 + 28n - 24n^2 + 32n^3)/3.

G.f.: (1+3x)^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)

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

CROSSREFS

Cf. 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 July 12 21:31 EDT 2020. Contains 335669 sequences. (Running on oeis4.)