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
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).
Programs
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Magma
[(3+28*n-24*n^2+32*n^3)/3: n in [0..40]]; // Vincenzo Librandi, Nov 16 2011
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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 *) -
Sage
[(3+28*n-24*n^2+32*n^3)/3 for n in (0..40)] # G. C. Greubel, May 26 2021
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