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%I #55 Sep 16 2019 04:31:44
%S 6,666,5656566,555665666566566,5555555666655656666556566566566,
%T 555555555555555666666665555665666666666555566566666556566566566
%N a(n) is the A325907(n)-th triangular number.
%C a(n) decimal expansion includes A141023(n-1) 5's and A052950(n) 6's in digits.
%C All terms are elements of A213516.
%H Seiichi Manyama, <a href="/A309597/b309597.txt">Table of n, a(n) for n = 1..9</a>
%F a(n) = A000217(A325907(n)).
%F a(n) = A093142(2^n - 1) + A325493(n-1) + A325910(n-1) * 10^(2^(n-1)).
%e a(1) = 6 = 6 + 0 + 0 * 10^1.
%e a(2) = 666 = 556 + 10 + 1 * 10^2.
%e a(3) = 5656566 = 5555556 + 1010 + 10 * 10^4.
%e a(4) = 555665666566566 = 555555555555556 + 11011010 + 1101 * 10^8.
%e ------------------------------------------------------------------
%e a(2) = 6 6 6. ( 3 6's)
%e - -
%e a(3) = 5 65 65 66. ( 3 5's and 4 6's)
%e - -- --
%e a(4) = 555 6656 6656 6566. ( 6 5's and 9 6's)
%e --- ---- ----
%e a(5) = 5555555 66665565 66665565 66566566. (15 5's and 16 6's)
%e ------- -------- --------
%o (Ruby)
%o def A325907(n)
%o a = [3]
%o (2..n).each{|i|
%o j = 10 ** (2 ** (i - 2))
%o a << (j + 3) * (j - 1) / 3 - a[-1]
%o }
%o a
%o end
%o def A309597(n)
%o A325907(n).map{|i| i * (i + 1) / 2}
%o end
%o p A309597(10)
%Y Cf. A000217, A052950, A093142, A141023, A213516, A325907, A325910, A325493.
%K nonn
%O 1,1
%A _Seiichi Manyama_, Sep 14 2019
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