A330983 Alternatively add and multiply pairs of the nonnegative integers.

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, ....

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (0,3,0,-3,0,1).

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

Adjacent sequences: A330980 A330981 A330982 * A330984 A330985 A330986

Keyword

nonn,easy

Author

George E. Antoniou, Jan 05 2020

Status

approved