A377917 Number of n-digit terms in A377912.

10, 66, 489, 3631, 26951, 200045, 1484850, 11021410, 81807240, 607220362, 4507138581, 33454573430, 248319075015, 1843166918425, 13681044394077, 101548575900358, 753751904485831, 5594779921615960, 41527672679871145, 308242258385100002, 2287951231622970075, 16982489246315828049

Offset: 1

Author

Sebastian Karlsson and N. J. A. Sloane, Nov 30 2024

Keywords

• nonn
• base
• easy

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

Examples

			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.
		

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).

Crossrefs

Cf. A342042, A377912.

First differences of A377918.

Programs

Mathematica

LinearRecurrence[{5, 15, 20, 15, 6, 1}, {10, 66, 489, 3631, 26951, 200045, 1484850}, 25] (* Paolo Xausa, Dec 01 2024 *)

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)

Extensions

a(6) and beyond from Michael S. Branicky, Nov 30 2024