OFFSET
1,2
COMMENTS
If b(n) is the n-th octagonal number multiple of 32 then a(n) = b(n)/8.
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).
FORMULA
O.g.f.: 4*x^2*(3 + 20*x + 15*x^2 + 10*x^3)/((1 + x)^2*(1 - x)^3).
E.g.f.: (33 - 32*x + 24*x^2)*exp(x) + (7 + 6*x)*exp(-x) - 40.
a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5).
a(n) = 8*n*(3*n - 7) - (6*n - 7)*(-1)^n + 33.
From Colin Barker, Jan 20 2018: (Start)
a(n) = 24*n^2 - 62*n + 40 for n even.
a(n) = 24*n^2 - 50*n + 26 for n odd. (End)
EXAMPLE
A000326(8) = 92 is in the sequence because 92 = 4*23.
MAPLE
P:=proc(n) local x; x:=n*(3*n-1)/2; if x mod 4=0 then x; fi; end:
seq(P(i), i=0..2*10^2); # Paolo P. Lava, Jan 19 2018
MATHEMATICA
Table[8 n (3 n - 7) - (6 n - 7) (-1)^n + 33, {n, 1, 50}]
(* Second program (using definition): *)
Select[Table[k*(3*k - 1)/2, {k, 0, 200}], Divisible[#, 4]&] (* Jean-François Alcover, Jan 19 2018 *)
PROG
(PARI) vector(50, n, nn; 8*n*(3*n-7)-(6*n-7)*(-1)^n+33)
(Sage) [8*n*(3*n-7)-(6*n-7)*(-1)^n+33 for n in (1..50)]
(Maxima) makelist(8*n*(3*n-7)-(6*n-7)*(-1)^n+33, n, 1, 50);
(Magma) [8*n*(3*n-7)-(6*n-7)*(-1)^n+33: n in [1..50]];
(GAP) List([1..50], n -> 8*n*(3*n-7)-(6*n-7)*(-1)^n+33);
(PARI) concat(0, Vec(4*x^2*(3 + 20*x + 15*x^2 + 10*x^3) / ((1 - x)^3*(1 + x)^2) + O(x^40))) \\ Colin Barker, Jan 20 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Bruno Berselli, Jan 18 2018
STATUS
approved