OFFSET
0,2
COMMENTS
For an origin of this sequence, see the numerical spiral illustrated in the Links section.
LINKS
Bruno Berselli, Table of n, a(n) for n = 0..1000
Bruno Berselli, Illustration of initial terms.
Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).
FORMULA
O.g.f.: (1 + 4*x + 3*x^2 - x^3)/((1 + x)^2*(1 - x)^3).
E.g.f.: (1/16)*((21 + 56*x + 14*x^2)*exp(x) - (5 + 2*x)*exp(-x)). - G. C. Greubel, Aug 19 2017
a(n) = A195020(n) + n + 1.
a(n) - a(-n-1) = A047336(n+1).
a(n+1) - a(-n) = A113804(n+1).
a(n+2) - a(n) = A047385(n+3).
a(n+4) - a(n) = A113803(n+4).
a(2*n) + a(2*n-1) = A069127(n+1).
a(2*n) - a(2*n-1) = A016813(n).
a(2*n+1) - a(2*n) = A016777(n+1).
a(n+2) + 2*a(n+1) + a(n) = A024966(n+2).
MATHEMATICA
Table[(14*n*(n + 3) + (2*n - 5)*(-1)^n + 21)/16, {n, 0, 50}] (* Vincenzo Librandi, Mar 26 2013 *)
LinearRecurrence[{1, 2, -2, -1, 1}, {1, 5, 10, 17, 26}, 60] (* Harvey P. Dale, Jun 19 2020 *)
PROG
(PARI) for(n=0, 50, print1((14*n*(n+3)+(2*n-5)*(-1)^n+21)/16", "));
(Magma) [(14*n*(n+3)+(2*n-5)*(-1)^n+21)/16: n in [0..50]];
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Bruno Berselli, Oct 20 2011 - based on remarks and sequences by Omar E. Pol
STATUS
approved