OFFSET
1,2
COMMENTS
Central terms of A170950, seen as a triangle of rows with an odd number of terms.
Equivalently, numbers of the form m*(4*m+3)+1, where m = 0, -1, 1, -2, 2, -3, 3, ... . - Bruno Berselli, Jan 05 2016
LINKS
Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).
FORMULA
a(n+3) - a(n+2) - a(n+1) + a(n) = A010696(n+1).
a(n) = A193868(n)/2. - Omar E. Pol, Aug 16 2011
G.f.: -x*(1+x+4*x^2+x^3+x^4) / ( (1+x)^2*(x-1)^3 ). - R. J. Mathar, Aug 18 2011
E.g.f.: ((2 + x + 2*x^2)*cosh(x) + (1 - x + 2*x^2)*sinh(x) - 2)/2. - Stefano Spezia, Nov 16 2024
MATHEMATICA
Select[Table[(n (n + 1)/2 + 1)/2, {n, 600}], IntegerQ] (* Vladimir Joseph Stephan Orlovsky, Feb 06 2012 *)
(Select[PolygonalNumber@ Range@ 100, OddQ] + 1 )/2 (* Version 10.4, or *)
Rest@ CoefficientList[Series[-x (1 + x + 4 x^2 + x^3 + x^4)/((1 + x)^2 (x - 1)^3), {x, 0, 50}], x] (* Michael De Vlieger, Jun 30 2016 *)
PROG
(PARI) a(n)=(2*n-1)*(2*n-1-(-1)^n)\4+1 \\ Charles R Greathouse IV, Jun 11 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Reinhard Zumkeller, Mar 08 2010
EXTENSIONS
New name from Omar E. Pol, Aug 16 2011
STATUS
approved