This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A330510 #26 Jan 07 2024 16:34:39
%S A330510 2,3,3,4,10,4,5,22,22,5,6,40,70,40,6,7,65,171,171,65,7,8,98,356,534,
%T A330510 356,98,8,9,140,665,1373,1373,665,140,9,10,192,1148,3088,4246,3088,
%U A330510 1148,192,10,11,255,1866,6294,11257,11257,6294,1866,255,11
%N A330510 Triangle read by rows: T(n,k) is the number of ternary strings of length n+1 with k+1 indispensable digits and a nonzero leading digit, with 0 <= k <= n.
%C A330510 A digit in a string is called indispensable if it is greater than the following digit or equal to the following digits which are eventually greater than the following digit. We also assume that there is an invisible digit 0 at the end of any string. For example, in 7233355548, the digits 7, 5, 5, 5, and 8 are indispensable.
%C A330510 T(n, k) is also the number of integers m where the length of ternary representation of m is n+k and the digit sum of the ternary representation of 2m is 2(k+1).
%H A330510 Andrew Howroyd, <a href="/A330510/b330510.txt">Table of n, a(n) for n = 0..1325</a> (rows 0..50)
%H A330510 J. Y. Choi, <a href="https://doi.org/10.7546/nntdm.2019.25.2.40-48">Indispensable digits for digit sums</a>, Notes Number Theory Discrete Math 25 (2019), pp. 40-48.
%H A330510 J. Y. Choi, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL22/Choi/choi15.html">Digit sums generalizing binomial coefficients</a>, J. Integer Seq. 22 (2019), Article 19.8.3.
%F A330510 T(n, k) = A330381(n+1, k+1) - A330381(n, k+1).
%e A330510 Triangle begins
%e A330510 2;
%e A330510 3, 3;
%e A330510 4, 10, 4;
%e A330510 5, 22, 22, 5;
%e A330510 6, 40, 70, 40, 6;
%e A330510 7, 65, 171, 171, 65, 7;
%e A330510 ...
%e A330510 There are 4 strings (100, 112, 120, 200) of length 3 with 1 indispensable digits and a nonzero leading digit.
%e A330510 There are 10 strings (101, 102, 110, 121, 122, 201, 202, 210, 212, 220) of length 3 with 2 indispensable digits are a nonzero leading digit.
%e A330510 There are 4 strings (111, 211, 221, 222) of length 3 with 3 indispensable digits and a nonzero leading digit.
%e A330510 Hence T(2,0)=4, T(2,1)=10, T(2,2)=4.
%o A330510 (PARI)
%o A330510 A027907(n, k) = if(n<0, 0, polcoef((1 + x + x^2)^n, k));
%o A330510 T(n,k) = {A027907(n+1, 2*k+1) + A027907(n+1, 2*k+2) - A027907(n, 2*k+1) - A027907(n, 2*k+2)} \\ _Andrew Howroyd_, Dec 20 2019
%Y A330510 Cf. A005773, A330381, A027907.
%K A330510 nonn,tabl,base
%O A330510 0,1
%A A330510 _Ji Young Choi_, Dec 16 2019