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A325983 Row sums of the triangle A325982. 1
1, 1, 2, 2, 5, 5, 18, 21, 77, 102, 337, 480, 1449, 2155, 6107, 9348, 25355, 39639, 104188, 165596, 425156, 684926, 1726737, 2813582, 6990175, 11501905, 28232753, 46854161, 113841632, 190362483, 458480128, 771855377, 1844765161, 3124639626, 7417428613, 12633074088 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..36.

FORMULA

a(n) = Sum_{k=0..floor((n-1)/2)} binomial(n - 1, k - 1) - binomial(n - k - 1, k - 1) + 1.

a(n) = Sum_{k=0..A004526(n-1)} A007318(n - 1, k - 1) - A007318(n - k - 1, k - 1) + 1.

MAPLE

a := n -> add(binomial(n-1, k-1)-binomial(n-k-1, k-1)+1, k = 0 .. floor((n-1)/2)): seq(a(n), n = 1 .. 40);

MATHEMATICA

a[n_]:=Sum[T[n, k], {k, 0, Floor[(n-1)/2]}]; Array[a, 40]

PROG

(GAP) List([1..40], n->Sum([0..Int((n-1)/2)], k->Binomial(n-1, k-1)-Binomial(n-k-1, k-1)+1));

(MAGMA) [(&+[Binomial(n-1, k-1)-Binomial(n-k-1, k-1)+1: k in [0..Floor((n-1)/2)]]): n in [1..40]];

(PARI) a(n) = sum(k=0, floor((n-1)/2), binomial(n - 1, k - 1) - binomial(n - k - 1, k - 1) + 1);

CROSSREFS

Cf. A004526, A007318, A325982.

Sequence in context: A245844 A083849 A326512 * A063501 A103892 A000403

Adjacent sequences:  A325980 A325981 A325982 * A325984 A325985 A325986

KEYWORD

nonn

AUTHOR

Stefano Spezia, May 29 2019

STATUS

approved

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Last modified January 28 03:49 EST 2020. Contains 331317 sequences. (Running on oeis4.)