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 A130517 Triangle read by rows: row n counts down from n in steps of 2, then counts up the remaining elements in the set {1,2,...n}, again in steps of 2. 26
 1, 2, 1, 3, 1, 2, 4, 2, 1, 3, 5, 3, 1, 2, 4, 6, 4, 2, 1, 3, 5, 7, 5, 3, 1, 2, 4, 6, 8, 6, 4, 2, 1, 3, 5, 7, 9, 7, 5, 3, 1, 2, 4, 6, 8, 10, 8, 6, 4, 2, 1, 3, 5, 7, 9, 11, 9, 7, 5, 3, 1, 2, 4, 6, 8, 10, 12, 10, 8, 6, 4, 2, 1, 3, 5, 7, 9, 11, 13, 11, 9, 7, 5, 3, 1, 2, 4, 6, 8, 10, 12, 14, 12, 10 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Triangle read by rows in which row n lists the number of pairs of states of the subshells of the n-th shell of the nuclear shell model ordered by energy level in increasing order. Row n lists a permutation of the first n positive integers. If n is odd then row n lists the first (n+1)/2 odd numbers in decreasing order together with the first (n-1)/2 positive even numbers. If n is even then row n lists the first n/2 even numbers in decreasing order together with the first n/2 odd numbers. LINKS Reinhard Zumkeller, Rows n = 1..120 of triangle, flattened Boris Putievskiy, Transformations [of] Integer Sequences And Pairing Functions, 2012, arXiv:1212.2732 [math.CO]. FORMULA a(n) = A162630(n)/2. - Omar E. Pol, Sep 02 2012 T(1,1)=1, for n>1: T(n,1)=T(n-1,1)+1 and T(n,k)=T(n-1,n-k+1), 1 (head row + 1) : reverse row) [1] -- Reinhard Zumkeller, Dec 03 2012 CROSSREFS Absolute values of A056951. Column 1 is A000027. Row sums are in A000217. Cf. A130556, A130598, A130602. Other versions are A004736, A212121, A213361, A213371. Cf. A028310 (right edge), A000012 (central terms), A220073 (mirrored), A220053 (partial sums in rows). Sequence in context: A087295 A175344 A056951 * A316715 A130212 A133737 Adjacent sequences:  A130514 A130515 A130516 * A130518 A130519 A130520 KEYWORD nonn,tabl,easy AUTHOR Omar E. Pol, Aug 08 2007 STATUS approved

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Last modified May 18 23:31 EDT 2022. Contains 353826 sequences. (Running on oeis4.)