A014942 a(n) = (1 + 24^n*(23*n - 1))/529.
1, 49, 1777, 57073, 1715953, 49491697, 1387212529, 38078983921, 1028756811505, 27446832213745, 724884022832881, 18985057740861169, 493749574409596657, 12764586312924606193, 328300388160453422833, 8406016915457191128817, 214387788361524002631409, 5448748098049810036109041
Offset: 1
Links
- Index entries for linear recurrences with constant coefficients, signature (49,-624,576).
Crossrefs
Cf. A014960.
Programs
-
Mathematica
a[1] = 1; a[n_Integer] := a[n - 1] + n*24^(n - 1); Table[ a[n], {n, 1, 20}] -
PARI
Vec(-x/((x-1)*(24*x-1)^2) + O(x^19)) \\ Elmo R. Oliveira, May 18 2025
Formula
a(n) = a(n-1) + n*24^(n-1).
a(n)= 49*a(n-1) - 624*a(n-2) + 576*a(n-3) for n > 3.
G.f.: x/((1-x)*(1-24*x)^2). - Joerg Arndt, May 23 2010
From Elmo R. Oliveira, May 18 2025: (Start)
E.g.f.: exp(x)*(1 + exp(23*x)*(552*x - 1))/529.
a(n) = 48*a(n-1) - 576*a(n-2) + 1 for n > 2. (End)
Extensions
More terms from Robert G. Wilson v, Sep 15 2000
Exchanged Lava formula of Jan 2009 with the definition [R. J. Mathar, May 23 2010]