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A014827 a(1)=1, a(n) = 5*a(n-1) + n. 12
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
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.
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 range(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
Sequence in context: A128726 A346395 A055146 * A141845 A048437 A099461
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified March 28 17:25 EDT 2024. Contains 371254 sequences. (Running on oeis4.)