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A014827 a(1)=1, a(n) = 5*a(n-1) + n. 11
1, 7, 38, 194, 975, 4881, 24412, 122068, 610349, 3051755, 15258786, 76293942, 381469723, 1907348629, 9536743160, 47683715816, 238418579097, 1192092895503, 5960464477534, 29802322387690, 149011611938471 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (7,-11,5).

FORMULA

a(n) = (5^(n+1) - 4*n - 5)/16.

G.f.: x/((1-5*x)*(1-x)^2).

a(n) = Sum_{k=0..n} (n-k)*5^k = Sum_{k=0..n} k*5^(n-k). - Paul Barry, Jul 30 2004

a(n) = Sum_{k=0..n} binomial(n+2, k+2)*4^k [Offset 0]. - Paul Barry, Jul 30 2004

MAPLE

a:=n->sum((5^(n-j)-1^(n-j))/4, j=0..n): seq(a(n), n=1..21); # Zerinvary Lajos, Jan 04 2007

MATHEMATICA

Join[{a=1, b=7}, Table[c=6*b-5*a+1; a=b; b=c, {n, 60}]] (* Vladimir Joseph Stephan Orlovsky, Feb 06 2011 *)

PROG

(Sage) [(gaussian_binomial(n, 1, 5)-n)/4 for n in xrange(2, 23)] # Zerinvary Lajos, May 29 2009

(MAGMA) [(5^(n+1)-4*n-5)/16: n in [1..30]]; // Vincenzo Librandi, Aug 23 2011

CROSSREFS

Cf. A016218, A016208, A000392, A000225, A003462, A003463, A003464, A023000, A023001, A002452, A002275, A016123, A016125, A016256.

Sequence in context: A037605 A128726 A055146 * A141845 A048437 A099461

Adjacent sequences:  A014824 A014825 A014826 * A014828 A014829 A014830

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified October 22 09:57 EDT 2018. Contains 316433 sequences. (Running on oeis4.)