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A317790
a(n) = 2*a(n-1) - a(n-2) + a(n-4) - 2*(n-5) + a(n-6) for n>5, a(0)=a(1)=1, a(2)=a(3)=7, a(4)=13, a(5)=19.
1
1, 1, 7, 7, 13, 19, 31, 37, 49, 61, 79, 91, 109, 127, 151, 169, 193, 217, 247, 271, 301, 331, 367, 397, 433, 469, 511, 547, 589, 631, 679, 721, 769, 817, 871, 919, 973, 1027, 1087, 1141, 1201, 1261, 1327, 1387, 1453, 1519, 1591, 1657, 1729, 1801, 1879, 1951
OFFSET
0,3
COMMENTS
a(n) is b(2*n) in A215175.
FORMULA
G.f.: (1 - x + 6*x^2 - 6*x^3 + 5*x^4 + x^5) / ((1 - x)^3*(1 + x)*(1 + x^2)). - Colin Barker, Aug 07 2018
a(n+1) = a(n) + 6*A059169(n+1).
a(2*k+1) = A003215(k).
From Bruno Berselli, Jul 08 2018: (Start)
a(2*k) = A016921(A000982(k)). More generally:
a(n) = (6*n^2 + 3*(3 - 2*(-1)^(n/2))*(1 + (-1)^n) + 2)/8. (End)
MATHEMATICA
CoefficientList[Series[(1 - x + 6 x^2 - 6 x^3 + 5 x^4 + x^5)/((1 - x)^3*(1 + x) (1 + x^2)), {x, 0, 51}], x] (* Michael De Vlieger, Aug 07 2018 *)
Table[(6 n^2 + 3 (3 - 2 (-1)^(n/2)) (1 + (-1)^n) + 2)/8, {n, 0, 60}] (* Bruno Berselli, Aug 08 2018 *)
PROG
(PARI) Vec((1 - x + 6*x^2 - 6*x^3 + 5*x^4 + x^5) / ((1 - x)^3*(1 + x)*(1 + x^2)) + O(x^60)) \\ Colin Barker, Aug 07 2018
CROSSREFS
Cf. A003215, A059169, A131729 (reverse order), A215175.
Sequence in context: A072821 A038589 A332304 * A109539 A109541 A173314
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Aug 07 2018
EXTENSIONS
Incorrect term 837 replaced with 817 by Colin Barker, Aug 07 2018
More terms from Colin Barker, Aug 07 2018
STATUS
approved