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 A236112 Triangle read by rows: T(n,k), n>=1, k>=1, in which column k lists k+1 copies of the squares in nondecreasing order, and the first element of column k is in row k(k+1)/2. 16
 0, 0, 1, 0, 1, 0, 4, 0, 4, 1, 0, 9, 1, 0, 9, 1, 0, 16, 4, 0, 16, 4, 1, 0, 25, 4, 1, 0, 25, 9, 1, 0, 36, 9, 1, 0, 36, 9, 4, 0, 49, 16, 4, 1, 0, 49, 16, 4, 1, 0, 64, 16, 4, 1, 0, 64, 25, 9, 1, 0, 81, 25, 9, 1, 0, 81, 25, 9, 4, 0, 100, 36, 9, 4, 1, 0, 100, 36, 16, 4, 1, 0, 121, 36, 16, 4, 1, 0, 121, 49, 16, 4, 1, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,7 COMMENTS Gives an identity for the sum of remainders of n mod k, for k = 1,2,3,...,n. Alternating sum of row n equals A004125(n), i.e., sum_{k=1..A003056(n))} (-1)^(k-1)*T(n,k) = A004125(n). Row n has length A003056(n) hence the first element of column k is in row A000217(k). LINKS Table of n, a(n) for n=1..94. EXAMPLE Triangle begins: 0; 0; 1, 0; 1, 0; 4, 0; 4, 1, 0; 9, 1, 0; 9, 1, 0; 16, 4, 0; 16, 4, 1, 0; 25, 4, 1, 0; 25, 9, 1, 0; 36, 9, 1, 0; 36, 9, 4, 0; 49, 16, 4, 1, 0; 49, 16, 4, 1, 0; 64, 16, 4, 1, 0; 64, 25, 9, 1, 0; 81, 25, 9, 1, 0; 81, 25, 9, 4, 0; 100, 36, 9, 4, 1, 0; 100, 36, 16, 4, 1, 0; 121, 36, 16, 4, 1, 0; 121, 49, 16, 4, 1, 0; ... For n = 24 the 24th row of triangle is 121, 49, 16, 4, 1, 0 therefore the alternating row sum is 121 - 49 + 16 - 4 + 1 - 0 = 85 equaling A004125(24). CROSSREFS Cf. A000203, A000217, A000290, A003056, A004125, A120444, A196020, A211343, A228813, A231345, A231347, A235791, A235794, A236104, A236106, A237048, A237591, A237593, A261699. Sequence in context: A019201 A137660 A123583 * A226787 A140574 A010636 Adjacent sequences: A236109 A236110 A236111 * A236113 A236114 A236115 KEYWORD nonn,tabf AUTHOR Omar E. Pol, Jan 23 2014 STATUS approved

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Last modified December 10 09:31 EST 2023. Contains 367710 sequences. (Running on oeis4.)