OFFSET
1,1
COMMENTS
Also number of n-digit terms in A342042.
a(1149) has 1001 digits. - Michael S. Branicky, Nov 30 2024
The terms of A377912 as decimal digit strings are a regular language so can be counted using the transitions in a state machine matching those strings. - Kevin Ryde, Dec 01 2024
LINKS
Michael S. Branicky, Table of n, a(n) for n = 1..1148
Michael S. Branicky, Python program for A377917
Index entries for linear recurrences with constant coefficients, signature (5,15,20,15,6,1).
FORMULA
From Kevin Ryde, Dec 01 2024: (Start)
a(n) = 5*a(n-1) + 15*a(n-2) + 20*a(n-3) + 15*a(n-4) + 6*a(n-5) + a(n-6) for n>=8.
G.f.: -1 + x + (1+x)^4 / (1 - 5*x - 15*x^2 - 20*x^3 - 15*x^4 - 6*x^5 - x^6). (End)
EXAMPLE
The 66 two-digit terms in A377912 are
10,11,12,13,14,15,16,17,18,19,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,
38,39,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,67,68,69,70,71,72,73,74,
75,76,77,78,79,89,90,91,92,93,94,95,96,97,98,99.
There is an obvious division into 5 blocks of size 10 and blocks of sizes 7, 5, 3, and 1.
MATHEMATICA
LinearRecurrence[{5, 15, 20, 15, 6, 1}, {10, 66, 489, 3631, 26951, 200045, 1484850}, 25] (* Paolo Xausa, Dec 01 2024 *)
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Sebastian Karlsson and N. J. A. Sloane, Nov 30 2024
EXTENSIONS
a(6) and beyond from Michael S. Branicky, Nov 30 2024
STATUS
approved