A350851 Cumulative sums of the first ceiling(n/2)+1 elements of rows 0 to n in Pascal's triangle.

1, 3, 6, 13, 24, 50, 92, 191, 354, 736, 1374, 2860, 5370, 11182, 21090, 43909, 83112, 172958, 328340, 682862, 1299528, 2700820, 5150688, 10697070, 20437756, 42415272, 81170004, 168337168, 322613196, 668607412, 1283037084, 2657319103, 5105342946, 10567113352, 20323851054

Offset

0,2

Links

Table of n, a(n) for n=0..34.

Example

The first ceiling(n/2)+1 elements from the first four rows of Pascal's are:
     1
    1 1
   1 2
  1 3 3
So a(0)=1, a(1)=a(0)+1+1=3, a(2)=a(1)+1+2=6, a(3)=a(2)+1+3+3=13.

Prog

(Python)
seq=[]; prev=[]; total=0
for n in range(30):
  row=[1]
  last=int(n/2)
  for k in range(last):
    row.append(prev[k]+prev[k+1])
  if n%2==1:
    row.append(row[-1])
  prev=row
  total+=sum(row)
  seq.append(total)
print(seq)

Crossrefs

Cf. A007318, A116496 (for n>=2, first differences).

Sequence in context: A358905 A027999 A005196 * A320286 A032287 A199403

Adjacent sequences: A350848 A350849 A350850 * A350852 A350853 A350854

Keyword

nonn,easy

Author

J. Stauduhar, Jan 18 2022

Status

approved