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URL: https://oeis.org/A330983

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A330983
Alternatively add and multiply pairs of the nonnegative integers.
2
1, 6, 9, 42, 17, 110, 25, 210, 33, 342, 41, 506, 49, 702, 57, 930, 65, 1190, 73, 1482, 81, 1806, 89, 2162, 97, 2550, 105, 2970, 113, 3422, 121, 3906, 129, 4422, 137, 4970, 145, 5550, 153, 6162, 161, 6806, 169, 7482, 177, 8190, 185, 8930, 193, 9702, 201, 10506, 209
OFFSET
1,2
COMMENTS
In groups of two, add and multiply the integers: 0+1, 2*3, 4+5, 6*7, ....
FORMULA
From Colin Barker, Jan 05 2020: (Start)
G.f.: x*(1 + 6*x + 6*x^2 + 24*x^3 - 7*x^4 + 2*x^5) / ((1 - x)^3*(1 + x)^3).
a(n) = 3*a(n-2) - 3*a(n-4) + a(n-6) for n>6.
a(n) = (1/2)*(-1 + 5*(-1)^n - 2*(1 + 5*(-1)^n)*n + 4*(1+(-1)^n)*n^2).
(End)
E.g.f.: (2 + 4*x*(1 + x))*cosh(x) - (3 + 2*x)*sinh(x) - 2. - Stefano Spezia, Jan 05 2020 after Colin Barker
MATHEMATICA
a[n_]:=If[OddQ[n], 4n-3, 2(n-1)(2n-1)]; Array[a, 53] (* Stefano Spezia, Jan 05 2020 *)
PROG
(PARI) Vec(x*(1 + 6*x + 6*x^2 + 24*x^3 - 7*x^4 + 2*x^5) / ((1 - x)^3*(1 + x)^3) + O(x^50)) \\ Colin Barker, Jan 07 2020
CROSSREFS
Cf. A330987.
Interspersion of A017077 and A256833. - Michel Marcus, Jan 06 2020
Sequence in context: A004989 A147355 A154139 * A299914 A187998 A177181
KEYWORD
nonn,easy
AUTHOR
George E. Antoniou, Jan 05 2020
STATUS
approved