A377917 - OEIS

%I #29 Dec 01 2024 19:34:09

%S 10,66,489,3631,26951,200045,1484850,11021410,81807240,607220362,

%T 4507138581,33454573430,248319075015,1843166918425,13681044394077,

%U 101548575900358,753751904485831,5594779921615960,41527672679871145,308242258385100002,2287951231622970075,16982489246315828049

%N Number of n-digit terms in A377912.

%C Also number of n-digit terms in A342042.

%C a(1149) has 1001 digits. - _Michael S. Branicky_, Nov 30 2024

%C 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

%H Michael S. Branicky, <a href="/A377917/b377917.txt">Table of n, a(n) for n = 1..1148</a>

%H Michael S. Branicky, <a href="/A377917/a377917.py.txt">Python program for A377917</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (5,15,20,15,6,1).

%F From _Kevin Ryde_, Dec 01 2024: (Start)

%F 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.

%F 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)

%e The 66 two-digit terms in A377912 are

%e   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,

%e   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,

%e   75,76,77,78,79,89,90,91,92,93,94,95,96,97,98,99.

%e There is an obvious division into 5 blocks of size 10 and blocks of sizes 7, 5, 3, and 1.

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

%Y Cf. A342042, A377912.

%Y First differences of A377918.

%K nonn,base,easy,new

%O 1,1

%A _Sebastian Karlsson_ and _N. J. A. Sloane_, Nov 30 2024

%E a(6) and beyond from _Michael S. Branicky_, Nov 30 2024