A256137 a(2) = 1; a(3) = 4; for n >= 4, a(n) = 2 + Sum_{i=4..n} d(i), where d(i) = i for even i, d(i) = i-3 for odd i.

1, 4, 6, 8, 14, 18, 26, 32, 42, 50, 62, 72, 86, 98, 114, 128, 146, 162, 182, 200, 222, 242, 266, 288, 314, 338, 366, 392, 422, 450, 482, 512, 546, 578, 614, 648, 686, 722, 762, 800, 842, 882, 926, 968, 1014, 1058, 1106, 1152, 1202, 1250, 1302, 1352, 1406

Offset

2,2

Links

Colin Barker, Table of n, a(n) for n = 2..1000

Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).

Formula

a(2) = 1; a(3) = 4; for n >= 4, a(n) = 2 + Sum_{i=4..n} d(i), where d(i) = i for even i, d(i) = i-3 for odd i.

From Colin Barker, Jul 12 2015 and Aug 20 2015: (Start)

a(n) = (5+3*(-1)^n-4*n+2*n^2)/4 for n>3.

a(n) = (n^2-2*n+4)/2 for n even and n>3.

a(n) = (n^2-2*n+1)/2 for n odd and n>3.

a(n) = 2*a(n-1)-2*a(n-3)+a(n-4) for n>6.

G.f.: x^2*(2*x^5-5*x^4+2*x^3+2*x^2-2*x-1) / ((x-1)^3*(x+1)).

(End)

Mathematica

Prepend[Table[2 + Sum[If[EvenQ@ i, i, i - 3], {i, 3, n}], {n, 3, 48}], 1] (* Michael De Vlieger, Jul 12 2015 *)
Join[{1, 2, 6, 8, 14, 18}, LinearRecurrence[{2, 0, -2, 1}, {26, 32, 42, 50}, 50]] (* Vincenzo Librandi, Jul 16 2015 *)

Prog

(PARI) a=4; print1("1, ", a, ", "); for (n=4, 100, if (Mod(n, 2)==0, d=n, d=n-3); a=a+d; print1(a, ", "))
(PARI) Vec(x^2*(2*x^5-5*x^4+2*x^3+2*x^2-2*x-1)/((x-1)^3*(x+1)) + O(x^100)) \\ Colin Barker, Jul 12 2015 and Aug 20 2015
(PARI) a(n)=if(n<3, 1, (n^2-2*n)\2+2-(n%2)) \\ Charles R Greathouse IV, Jul 17 2015

Crossrefs

Sequence in context: A110974 A173180 A200077 * A116897 A293763 A246324

Adjacent sequences: A256134 A256135 A256136 * A256138 A256139 A256140

Keyword

nonn,easy

Author

Kival Ngaokrajang, Jul 11 2015

Status

approved