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A059734 Carryless 11^n base 10; a(n) is carryless sum of 10*a(n-1) and a(n-1).

%I A059734 #25 Aug 01 2025 00:13:22
%S A059734 1,11,121,1331,14641,150051,1650561,17155171,188606881,1964664691,
%T A059734 10500200501,115502205511,1260524250621,13865766756831,
%U A059734 141412323214141,1555535555355551,16000880008800061,176008680086800671
%N A059734 Carryless 11^n base 10; a(n) is carryless sum of 10*a(n-1) and a(n-1).
%C A059734 Subsequence of A002113. - _Chai Wah Wu_, Jul 30 2025
%H A059734 Seiichi Manyama, <a href="/A059734/b059734.txt">Table of n, a(n) for n = 0..999</a>
%H A059734 David Applegate, Marc LeBrun and N. J. A. Sloane, <a href="http://neilsloane.com/doc/carry1.pdf">Carryless Arithmetic (I): The Mod 10 Version</a>
%F A059734 a(n)=Sum[Mod[Binomial[n, m], 10]*10^m, {m, 0, n}]. - _Roger L. Bagula_ and _Gary W. Adamson_, Sep 14 2008
%e A059734 a(7)=17155171 since a(6)=1650561 and digits of a(7) are sum mod 10 of 1, 6+1=7, 5+6=1, 0+5=5, 5+0=5, 6+5=1, 1+6=7 and 1.
%t A059734 Table[Sum[Mod[Binomial[n, m], 10]*10^m, {m, 0, n}], {n, 0, 30}] (* _Roger L. Bagula_ and _Gary W. Adamson_, Sep 14 2008 *)
%o A059734 (PARI) a(n) = fromdigits(Vec(Pol(digits(11))^n)%10); \\ _Seiichi Manyama_, Mar 10 2023
%o A059734 (Python)
%o A059734 from math import comb, prod
%o A059734 from sympy.ntheory.modular import crt
%o A059734 from gmpy2 import digits
%o A059734 def A059734(n):
%o A059734     k, l = 0, len(s:=digits(n,5))
%o A059734     for m in range(n+1):
%o A059734         t = digits(m,5).zfill(l)
%o A059734         k = 10*k+crt([5,2],[prod(comb(int(s[i]),int(t[i]))%5 for i in range(l))%5,int(not ~n & m)])[0]
%o A059734     return k # _Chai Wah Wu_, Jul 30 2025
%Y A059734 Cf. A004520, A006940, A008975, A361351, A002113.
%K A059734 base,nonn
%O A059734 0,2
%A A059734 _Henry Bottomley_, Feb 20 2001