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 A328362 Triangle read by rows: T(n,k) is the sum of all parts k in all partitions of n into consecutive parts, (1 <= k <= n). 6
 1, 0, 2, 1, 2, 3, 0, 0, 0, 4, 0, 2, 3, 0, 5, 1, 2, 3, 0, 0, 6, 0, 0, 3, 4, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 8, 0, 2, 3, 8, 5, 0, 0, 0, 9, 1, 2, 3, 4, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 5, 6, 0, 0, 0, 0, 11, 0, 0, 3, 4, 5, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 6, 7, 0, 0, 0, 0, 0, 13, 0, 2, 3, 4, 5, 0, 0, 0, 0, 0, 0, 0, 0, 14 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Iff n is a power of 2 (A000079) then row n lists n - 1 zeros together with n. Iff n is an odd prime (A065091) then row n lists (n - 3)/2 zeros, (n - 1)/2, (n + 1)/2, (n - 3)/2 zeros, n. LINKS Table of n, a(n) for n=1..105. FORMULA T(n,k) = k*A328361(n,k). EXAMPLE Triangle begins: 1; 0, 2; 1, 2, 3; 0, 0, 0, 4; 0, 2, 3, 0, 5; 1, 2, 3, 0, 0, 6; 0, 0, 3, 4, 0, 0, 7; 0, 0, 0, 0, 0, 0, 0, 8; 0, 2, 3, 8, 5, 0, 0, 0, 9; 1, 2, 3, 4, 0, 0, 0, 0, 0, 10; 0, 0, 0, 0, 5, 6, 0, 0, 0, 0, 11; 0, 0, 3, 4, 5, 0, 0, 0, 0, 0, 0, 12; 0, 0, 0, 0, 0, 6, 7, 0, 0, 0, 0, 0, 13; 0, 2, 3, 4, 5, 0, 0, 0, 0, 0, 0, 0, 0, 14; 1, 2, 3, 8,10, 6, 7, 8, 0, 0, 0, 0, 0, 0, 15; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16; ... For n = 9 there are three partitions of 9 into consecutive parts, they are [9], [5, 4], [4, 3, 2], so the 9th row of triangle is [0, 2, 3, 8, 5, 0, 0, 0, 9]. CROSSREFS Row sums give A245579. Column 1 gives A010054, n => 1. Leading diagonal gives A000027. Cf. A000079, A001227, A065091, A138785, A204217, A237048, A237593, A266531, A285898, A285899, A285900, A285914, A286000, A286001, A299765, A328361. Sequence in context: A138262 A276990 A127510 * A158810 A129391 A129390 Adjacent sequences: A328359 A328360 A328361 * A328363 A328364 A328365 KEYWORD nonn,tabl AUTHOR Omar E. Pol, Oct 20 2019 STATUS approved

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Last modified June 16 14:12 EDT 2024. Contains 373430 sequences. (Running on oeis4.)