A023536 Convolution of natural numbers with A023532.

1, 2, 4, 7, 10, 14, 19, 25, 31, 38, 46, 55, 65, 75, 86, 98, 111, 125, 140, 155, 171, 188, 206, 225, 245, 266, 287, 309, 332, 356, 381, 407, 434, 462, 490, 519, 549, 580, 612, 645, 679, 714, 750, 786, 823, 861, 900, 940, 981, 1023, 1066, 1110, 1155

Offset

1,2

Comments

From Vladimir Letsko, Dec 18 2016: (Start)

Also, a(n) is the number of possible values for the number of diagonals in a convex polyhedron with n+3 vertices.

Let v>4 denote the number of vertices of convex polyhedra. The set of possible numbers of diagonals is the union of sets {(k-1)(v-k-4), ..., (k-1)(v-(k+6)/2)}, where 1 <= k <= floor((sqrt(8v-15)-5)/2), and the set {(k-1)(v-k-4), ..., (v-3)(v-4)/2}, where k = floor((sqrt(8v-15)-3)/2). Note that cardinalities of all sets of this union excluding the last one are consecutive triangular numbers. (End)

Links

Vladimir Letsko, Table of n, a(n) for n = 1..500

Formula

a(n) = (n(n + 5) - 4 )/2 - Sum_{k=2..n} floor(1/2 + sqrt(2(k + 2))). - Jan Hagberg (jan.hagberg(AT)stat.su.se), Oct 16 2002

From Paul Barry, May 24 2004: (Start)

a(n) = (n+1)(n+2)/2 - Sum_{k=1..n+1} floor((sqrt(8k+1)-1)/2);

a(n) = Sum_{k=1..n+1} k-floor((sqrt(8k+1)-1)/2). (End)

Crossrefs

Cf. A005230, A279681.

Sequence in context: A022776 A025704 A025710 * A196126 A024536 A177237

Adjacent sequences: A023533 A023534 A023535 * A023537 A023538 A023539

Keyword

nonn

Author

Clark Kimberling

Extensions

Corrected by Jan Hagberg (jan.hagberg(AT)stat.su.se), Oct 16 2002

Status

approved