A014829 a(1)=1, a(n) = 6*a(n-1) + n.

1, 8, 51, 310, 1865, 11196, 67183, 403106, 2418645, 14511880, 87071291, 522427758, 3134566561, 18807399380, 112844396295, 677066377786, 4062398266733, 24374389600416, 146246337602515, 877478025615110

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

László Tóth, On Schizophrenic Patterns in b-ary Expansions of Some Irrational Numbers, arXiv:2002.06584 [math.NT], 2020. See also Proc. Amer. Math. Soc. 148 (2020), 461-469.

Index entries for linear recurrences with constant coefficients, signature (8,-13,6).

Formula

a(n) = (6^(n+1) - 5*n - 6)/25. - Rolf Pleisch, Oct 25 2010

Binomial transform of x*(1+x)/(1-5*x), or A003948 with a leading 0. a(n) = Sum_{k=0..n} (n-k)*6^k = Sum_{k=0..n} k*6^(n-k); a(n) = Sum_{k=0..n} binomial(n+2, k+2)*5^k [Offset 0]. - Paul Barry, Jul 30 2004

From Colin Barker, Jun 03 2020: (Start)

G.f.: x / ((1 - x)^2*(1 - 6*x)).

a(n) = 8*a(n-1) - 13*a(n-2) + 6*a(n-3) for n>3.

(End)

Maple

a:=n->1/5*sum(6^j-1, j=1..n): seq(a(n), n=1..20); # Zerinvary Lajos, Jun 27 2007

Mathematica

Join[{a=1, b=8}, Table[c=7*b-6*a+1; a=b; b=c, {n, 60}]] (* Vladimir Joseph Stephan Orlovsky, Feb 06 2011 *)
nxt[{n_, a_}]:={n+1, 6a+n+1}; NestList[nxt, {1, 1}, 30][[All, 2]] (* Harvey P. Dale, Feb 12 2023 *)

Prog

(Magma) [(6^(n+1)-5*n-6)/25: n in [1..30]]; // Vincenzo Librandi, Aug 23 2011
(PARI) Vec(x / ((1 - x)^2*(1 - 6*x)) + O(x^25)) \\ Colin Barker, Jun 03 2020

Crossrefs

Sequence in context: A037697 A037606 A055147 * A048438 A348312 A295602

Adjacent sequences: A014826 A014827 A014828 * A014830 A014831 A014832

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved