OFFSET
0,1
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = 24*n^2 + 24*n + 6.
G.f.: 6*(1 + 6*x + x^2) / (1 - x)^3. - Colin Barker, Aug 05 2015
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Colin Barker, Aug 05 2015
a(n) = A032528(4*n+2). [Bruno Berselli, Aug 05 2015]
a(n)*(2*h-1)^2 = a((2*h-1)*n+h-1). For h=0, a(n) = a(-n-1); for h=7, 169*a(n) = a(13*n+6). [Bruno Berselli, Aug 05 2015]
EXAMPLE
By the definition, given a = 7 and b = 5*7+2 = 37, c = 7*7+3 = 52, it follows that a^2+a = 56, b^2+b = 1406, c^2+c = 2756, where 56, 1406, 2756 are in arithmetic progression. Therefore, 2756-1406 = 1406-56 = 1350 and 1350 is in the sequence (8th term).
MATHEMATICA
Table[24 n^2 + 24 n + 6, {n, 0, 40}] (* Bruno Berselli, Aug 05 2015 *)
LinearRecurrence[{3, -3, 1}, {6, 54, 150}, 50] (* Vincenzo Librandi, Aug 05 2015 *)
PROG
(PARI) Vec(6*(1+6*x+x^2)/(1-x)^3 + O(x^100)) \\ Colin Barker, Aug 05 2015
(Magma) [24*n^2+24*n+6: n in [0..40]]; // Vincenzo Librandi, Aug 05 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Marco Ripà, Aug 05 2015
STATUS
approved